Abstract
Syphilis is a sexually transmitted disease having different signs and symptoms with four main stages, namely primary, secondary, latent, and tertiary. Congenital (vertical) transmission of syphilis from infected mother to fetus or neonatal is still a cause of high perinatal morbidity and mortality. A model of transmission of syphilis with three different ways of transmission, namely vertical, heterosexual, and homosexual, is formulated as a system of nonlinear ordinary differential equations. Treatment is also incorporated at various stages of infection. Total male and female population is divided in various classes (i.e., were susceptible, exposed, primary and secondary infected, early and late latent, tertiary, infected treated, latent treated, infected child [newborn], and treated infected child [at birth time]). Stability of disease-free equilibrium and endemic equilibrium is established. Control treatment is applied. It is observed that safe sexual habits and controlled treatment in each stage including pregnancy are effective parameters to curb disease spread.
TopIntroduction
Syphilis is a sexually transmitted disease caused by infection from bacteria Treponema pallidum (T. pallidum). Treponema pallidum is a spirochete bacterium usually transmitted by sexual contact through exposure to mucocutaneous syphilitic lesions. Wright and Jones (2003) have observed that in body fluid the infecting organism starts to replicate locally. As per WHO (2007) report, annually 12 million active infections of syphilis are getting reported. According to CDC (2010) report, there were total 13,774 cases of primary and secondary syphilis reported during 2010. Values et al. (2000) have reported that about 30 to 50% of individuals suffering from primary or secondary syphilis are at serious risk of spreading disease through sexual contacts. They also have observed that more than 80% of women with syphilis are in their reproductive (20 to 35 years old) age which causes high risk of congenital transmission. Walker and Walker (2002) have observed that each year high numbers of pregnancies are getting badly affected in all over world and yearly around 4,60,000 pregnancies end in abortion and 2,70,000 babies born prematurely or with low birth weight because of maternal syphilis. As per CDC (2010) report, rates of female and congenital syphilis were increased during 2005-2008 in the USA. In 2008, WHO estimated that 1.9 million pregnant women had active syphilis. Stolte et al. (2001), Simms et al. (2005), Heffelfinger et al. (2007) and Read et al. (2015) have reported revival of syphilis amongst homosexual male population in early 2000 even though overall decrease is reported from 1990.
In 2006, lifetime medical cost per case of syphilis was estimated as $572. Chesson et al. (2008) observed that the treatment cost per case could get increased in case of congenital infection. Blandford and Gift (2003) suggested early stage treatment to reduce the cost per case as early stage treatment is less expensive than treatment for later stage disease.